{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:GYQAUM2OKGS533ZYGXVOY5GIL5","short_pith_number":"pith:GYQAUM2O","canonical_record":{"source":{"id":"2401.01745","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-01-03T13:41:58Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6f3e829388f1374abbcb33fef048c7776bcb9e5b3780168fd287a601f3b1c66f","abstract_canon_sha256":"f767d3451c7658f95580f528071a75e3a00bffcc3079b190c637c981654ce88f"},"schema_version":"1.0"},"canonical_sha256":"36200a334e51a5ddef3835eaec74c85f594d27de1703458467b51b6d1a94157d","source":{"kind":"arxiv","id":"2401.01745","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.01745","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"2401.01745v3","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.01745","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"GYQAUM2OKGS5","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"pith_short_16","alias_value":"GYQAUM2OKGS533ZY","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"pith_short_8","alias_value":"GYQAUM2O","created_at":"2026-07-05T08:35:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:GYQAUM2OKGS533ZYGXVOY5GIL5","target":"record","payload":{"canonical_record":{"source":{"id":"2401.01745","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-01-03T13:41:58Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6f3e829388f1374abbcb33fef048c7776bcb9e5b3780168fd287a601f3b1c66f","abstract_canon_sha256":"f767d3451c7658f95580f528071a75e3a00bffcc3079b190c637c981654ce88f"},"schema_version":"1.0"},"canonical_sha256":"36200a334e51a5ddef3835eaec74c85f594d27de1703458467b51b6d1a94157d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:35:40.403267Z","signature_b64":"TwdOtSXwV+ESbyYBn3w8PnK8W1JpKDWDyRJkEp3JbGuEaX9MXn/47PBD67WOXOZHuxQyF/se2Z5KL9HAW67YDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36200a334e51a5ddef3835eaec74c85f594d27de1703458467b51b6d1a94157d","last_reissued_at":"2026-07-05T08:35:40.402870Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:35:40.402870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.01745","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:35:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1AeHj9qCwDq6hDTXNJzElJ1pwKAtrtgJ7oxSqLf6WWwcUt7lnZXEKMBs1MYPqnwQvwbOkZT348YhGW9sAykRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:43:46.592017Z"},"content_sha256":"410962cc79fc1f4c9327984fc0144b60b1c58c48c4a4c63fabe20c15d19b3872","schema_version":"1.0","event_id":"sha256:410962cc79fc1f4c9327984fc0144b60b1c58c48c4a4c63fabe20c15d19b3872"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:GYQAUM2OKGS533ZYGXVOY5GIL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Giacomo Rosilho de Souza, Marcus J. Grote, Rolf Krause, Simone Pezzuto","submitted_at":"2024-01-03T13:41:58Z","abstract_excerpt":"Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01745","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.01745/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:35:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IodzUJTCYi3xyTocRc1H7eWNP1Ff4KiWHYYmHTPOoeMWqPP2yLqC/y8TNz3+LdraFl+Ou49IpV/G4HNIymyUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:43:46.592412Z"},"content_sha256":"4213f69f1b8a2d573d301ecd079178c386e67c472cd6386ecd02c27b8163f7ce","schema_version":"1.0","event_id":"sha256:4213f69f1b8a2d573d301ecd079178c386e67c472cd6386ecd02c27b8163f7ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYQAUM2OKGS533ZYGXVOY5GIL5/bundle.json","state_url":"https://pith.science/pith/GYQAUM2OKGS533ZYGXVOY5GIL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYQAUM2OKGS533ZYGXVOY5GIL5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T14:43:46Z","links":{"resolver":"https://pith.science/pith/GYQAUM2OKGS533ZYGXVOY5GIL5","bundle":"https://pith.science/pith/GYQAUM2OKGS533ZYGXVOY5GIL5/bundle.json","state":"https://pith.science/pith/GYQAUM2OKGS533ZYGXVOY5GIL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYQAUM2OKGS533ZYGXVOY5GIL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:GYQAUM2OKGS533ZYGXVOY5GIL5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f767d3451c7658f95580f528071a75e3a00bffcc3079b190c637c981654ce88f","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-01-03T13:41:58Z","title_canon_sha256":"6f3e829388f1374abbcb33fef048c7776bcb9e5b3780168fd287a601f3b1c66f"},"schema_version":"1.0","source":{"id":"2401.01745","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.01745","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"2401.01745v3","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.01745","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"GYQAUM2OKGS5","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"pith_short_16","alias_value":"GYQAUM2OKGS533ZY","created_at":"2026-07-05T08:35:40Z"},{"alias_kind":"pith_short_8","alias_value":"GYQAUM2O","created_at":"2026-07-05T08:35:40Z"}],"graph_snapshots":[{"event_id":"sha256:4213f69f1b8a2d573d301ecd079178c386e67c472cd6386ecd02c27b8163f7ce","target":"graph","created_at":"2026-07-05T08:35:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2401.01745/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments ar","authors_text":"Giacomo Rosilho de Souza, Marcus J. Grote, Rolf Krause, Simone Pezzuto","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-01-03T13:41:58Z","title":"Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.01745","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:410962cc79fc1f4c9327984fc0144b60b1c58c48c4a4c63fabe20c15d19b3872","target":"record","created_at":"2026-07-05T08:35:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f767d3451c7658f95580f528071a75e3a00bffcc3079b190c637c981654ce88f","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-01-03T13:41:58Z","title_canon_sha256":"6f3e829388f1374abbcb33fef048c7776bcb9e5b3780168fd287a601f3b1c66f"},"schema_version":"1.0","source":{"id":"2401.01745","kind":"arxiv","version":3}},"canonical_sha256":"36200a334e51a5ddef3835eaec74c85f594d27de1703458467b51b6d1a94157d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36200a334e51a5ddef3835eaec74c85f594d27de1703458467b51b6d1a94157d","first_computed_at":"2026-07-05T08:35:40.402870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:35:40.402870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TwdOtSXwV+ESbyYBn3w8PnK8W1JpKDWDyRJkEp3JbGuEaX9MXn/47PBD67WOXOZHuxQyF/se2Z5KL9HAW67YDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:35:40.403267Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.01745","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:410962cc79fc1f4c9327984fc0144b60b1c58c48c4a4c63fabe20c15d19b3872","sha256:4213f69f1b8a2d573d301ecd079178c386e67c472cd6386ecd02c27b8163f7ce"],"state_sha256":"31e6784b4f09d7f6e341c8d52243da98a2e80a536e5523eef1b21645dffa9834"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TVkxdlKDqz9MGHHqwxKwARQpc15U+TXnClC11zkIL0YdSVWd0R4+iOD+x1ay7QwNZ8tDi/4arfh84VEBjdmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:43:46.594354Z","bundle_sha256":"c17e5bafc76b50fd628065ca0be72f47fa2b22f1cfc8807ab68971f35fadd503"}}